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We introduce Reverse Derivative Ascent: a categorical analogue of gradientbased methods for machine learning. Our algorithm is defined at the level ofso-called reverse differential categories. It can be used to learn theparameters of models which are expressed as morphisms of such categories. Ourmotivating example is boolean circuits: we show how our algorithm can beapplied to such circuits by using the theory of reverse differentialcategories. Note our methodology allows us to learn the parameters of booleancircuits directly, in contrast to existing binarised neural network approaches.Moreover, we demonstrate its empirical value by giving experimental results onbenchmark machine learning datasets.

Reverse Derivative Ascent: A Categorical Approach to Learning Boolean Circuits